Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.     

Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.     

New exact solutions of Einstein—Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

Mapping of muscle deformation during heating: in situ dynamic MRI and nonlinear registration

We present developments in dynamic magnetic resonance imaging that allow internal structural muscle markers to be followed during heating. This monitoring is based on quantitative characterization of the experimental conditions and their temperature time course. A nonlinear image registration technique was optimized and applied to consecutively acquired images to measure the deformation fields in the muscle. A model coupling local deformation and temperature was obtained, which for the first time takes into account the variations of deformation and temperature in the sample. This modeling opens the way to a better understanding of the mechanisms responsible for mass loss and degradation of the textural properties of muscle during heating.     

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

色噪声对光学双稳态的影响

采用统一色噪声近似构建了由乘法色噪声驱动的纯吸收型光学双稳态状态方程,并分析了色噪声对光学双稳态的影响,将结果与白噪声驱动的光学双稳态进行比较.结果表明:当乘法噪声与加法噪声处在正关联时,增加乘法色噪声的自关联时间r,光学双稳性的区域显著变宽,即磁滞回线面积变大;当乘法噪声与加法噪声处在负关联时,只有乘法噪声较小时,改变乘法色噪声的自关联时间r,光学双稳态才发生改变;当乘法噪声的自相关时间等于零时,本文模型退化为乘法白噪声驱动的光学双稳性状态方程.     

On the oscillons in the signum-Gordon model

New periodic solutions of signum-Gordon equation are presented. We first find solutions φ₀(x, t) defined for (x, t) ∈ ? × [0, T ] and satisfying the condition φ₀(x, 0) = φ₀(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).     

227-W output all-fiberized Tm-doped fiber laser at 1908 nm

In this paper, we report that a diode-pumped thulium-doped double clad silica fiber laser can provide powers of up to 227 W at 1908 nm, corresponding to a slope efficiency of 54.3%, and an optical-to-optical efficiency of 51.2%. The output power, to the best of our knowledge, is the highest output at 1908 nm. The beam quality M2 factor is about 1.56. Also discussed in this paper is the dependence of the laser performance on fiber length.